First a bit of background or context -- just in case you didn't know.
So apparently, as well as the suttas, there's something called the vinaya i.e. the code of Monastic discipline. These are (or include) many of dozens of rules which the Buddha established for monks -- and "following the vinaya" is one of the things that a monk is supposed to do (and affects or defines whether someone is considered to be a monk).
The (codified) vinaya defines the letter-of-the-law of what monks must or mustn't do. I only know some details and vague outlines but I think it amounts to something including this (and more) ...
- No handling money
- No secular "job"
- Maybe a limited acceptance of secular authorities (e.g. perhaps no secular "boss")
- No selling the Dhamma (no secular "clients")
- Limited interaction with lay-folk
... so "psychotherapy service" doesn't quite sound like what a monk should do -- e.g. I wouldn't expect to look up "psychotherapy" in the Yellow Pages and find a Buddhist monk advertising there.
People also have an ideal (perhaps idiosyncratic or judgemental) of what a monk should do, I think it's something like ...
- If you're interested in Buddhism you go to a monastery for training
- Monks teach Buddhism to novices (i.e. monk-candidates), to lay people who are taking "retreats", and the occasional Dhamma-talk (like an academic "lecture" on a subject) to a group of people when invited
- Monks take their bowl e.g. to the local village or onto the public street once a day, where people may put food in the bowl, but that's a silent transaction (or not transactional)
... so limited opportunity for any one-on-one -- and, "providing a service" to lay-people isn't entirely what being a monk is about. To the contrary, it's lay people who should provide some service to the sangha, doing or providing things which monks may need but aren't allowed to do themselves (including storing food, buying any goods and services, and so on).
Incidentally some people observe that the present actuality isn't as ideal as the outline above, in many Buddhist countries -- e.g. that some monasteries (or temples) do collect money, that monks live luxuriously, that there are "superstitions" or "folk religions" mixed in, that monks seem to make a living by showing up at lay funerals, and so on.
But anyway the content of the Vinaya -- the letter of the law if not the spirit -- varies quite little I think, over the centuries and over continents. Monks are expected to memorise it and recite it regularly.
Still there are deviations, in particular I think it's difficult to practice ...
- When there's no support or cooperation from lay society (e.g. where the lay society isn't Buddhist and isn't prepared to support a monastic society)
- When there's hostility from the secular powers (e.g. when the emperor thinks that Buddhist monks have become a drain on the empire's or the provinces' ability to raise taxes and/or armies)
For these reasons the existence of the sangha is a bit precarious, and without the sangha i.e. without monks being able to live, Buddhism might not be viable. Other traditions develop e.g. monks work in the fields to help support themselves, etc.
There also "competition" from other religions -- Hinduism, Islam, Daoism, Folk religions (e.g. animism), not to mention Christianity (and, perhaps most recently, western Rationalism and/or Science) -- but that's not on-topic here.
Anyway I think that Japan -- Japanese Buddhism -- might be one of the more extreme examples of the Vinaya being modified by secular edict. So, for example, I think that Japanese senior abbots might even marry and so on. I can't comment on countries where Buddhism itself has become a secular power.
As a gross approximation I'd guess that the "ideal" I outlined above (e.g. keeping separate from lay society) is a "Theravada" (the "Way of the Elder monks") ideal, whereas mixing more with lay society might be more "Mahayana" (the "Great vehicle") -- though Andrei points out that in practice this is a great oversimplification (and perhaps or arguably not a genuine distinction at all).
Anyway, to get round to your question -- yes, I think there are: in some places.
You asked about "in Buddhism" -- and I'm not sure what that means ... e.g. "in traditional Buddhism", or "in modern Buddhism", "in what we know of original or early Buddhism".
But for example, there's Welcome to Kusala.org ...
Kusala Bhikshu - is a volunteer Buddhist chaplain for -- The UCLA Medical Center Spiritual Care Committee, the University Religious Conference at UCLA, and the Garden Grove Police Department. Rev. Kusala is active in the interreligious communities of both Los Angeles and Orange County. He lives/works at the IBMC teaching Buddhism and meditation.
Perhaps what you're looking for is a Buddhist "chaplain"?
If you're dying in hospital then the staff might ask you if you want a visit from a chaplain, and some people might want a Buddhist chaplain.
Another possibility is that what you're asking about is a "teacher" -- i.e. a teacher might talk with you one-on-one and so on.
Another possibility is that you are asking for a (e.g. clinical) psychotherapist, but a Buddhist one.
It's this which ties the first bit of this answer to the second, by the way:
Ven. Kusala Bhikshu (Thich Tam-Thien) is an American born Bhikshu (monk) ordained in the Zen Tradition of Vietnam.
Another (more famous) example of Vietnamese Zen in the west is Plum Village and Thich Nhat Hanh (I don't know whether that has anything to do with psychotherapeutic consulting though).
I don't know much more -- this suggests that the Vietnamese Zen tradition might be inclusive rather than exclusive, maybe not very dogmatic.
Also I hope the first bit of this answer might help to explain, amplify or give some context to the answers from Samana Johann and user12901.
This, I don't know, might be another example, it's a publisher's blurb about an author:
Bhikkhu Basnagoda Rahula
Bhikkhu Basnagoda Rahula, PhD, was born in Sri Lanka and became a Buddhist monk in childhood. He holds a Master's Degree in literature, and a doctorate in English. He serves the congregation at the Houston Buddhist Vihara, and teaches English at the University of Houston. He lives in Texas.
I don't know what "serving the congregation" there might mean exactly, but that might include something of what you're asking about (see also that book).
I think I've also seen it argued or imp[lied, though, that a monk who serves the community which supports them is therefore not a true monk.
My personal opinion is that, broadly, lay people will want you to function well or to improve your functioning within samsara -- conversely Buddhism might be about stopping samsara altogether -- consequently there may be some disconnect between the aims of lay society and "Buddhism".
I also think that anyone who wants to "stop" might be seen as dysfunctional, by "puthujjanas" and so on (people who aren't disinterested in what you do for them).
Wanting to stop might therefore be stigmatised as some symptom of mental illness -- ironic that stopping, if it's meant as a cure or therapy, should be mistaken for the disease.
I can only hope that any psychotherapist worth their salt, Buddhist or not, might have some patience for their client's best interest, advocate for their client/patient rather than only for society.
People tend to be pushed, not just by their society but by their family, to perform. I happened to read an extreme example of that recently, here:
In my country if I will become a homeless guy who don't want any money even à cents who looking for illumination I will send to psychiatrict hospital.
Asking for food when you made de choice to live without money is ok in bouddhisme and Indian for yogi. Not in my country.
And the weather...
That's actually a bit contrary to my limited experience (or at least, "in my country") of homelessness and psychiatric hospitals, it might help[ to illustrate a dichotomy though (possibly a false dichotomy).