Using std:: vector functions in Stan

Is it possible to use C++ vector functions in Stan?

We need more information to answer questions such as this. Technically, any time you declare an array in the Stan language such as

data {
  int N;
  int J;
  int y[N, J]; // uses std::vector<std::vector<int> >

it utilizes a std::vector in C++. Likewise anytime you declare a vector[N] it uses the Eigen library, which is also C++.

But I would guess your question is actually whether you can call a C++ function (perhaps involving a vector) from the Stan language, in which case the answer is yes. To do so using RStan, see

Correct, I’m interested in calling std vector functions like erase() and begin()

Then, yes you need to declare but not define a function the the correct signature in the functions block of your Stan program, define a C++ function that does whatever, and then when you go to compile it, specify the full path to the C++ file as a #include. All of that is briefly explained in the linked vignette.