Emacs allows for the definition of buffer regions that represent "clickable text", see "(elisp)Clickable Text". One type of clickable text is a button which can be programmatically activated (have its action executed) with the push-button function.
But there does not seem to be a function to programmatically activate other types of clickable text. This is a suggestion that such a function be added to Emacs. It would be similar to push-button but would account for all the ways clickable text can be activated. Right now it appears that non-button clickable text can be activated essentially only interactively, e.g. with a press of RET or mouse-2 or invocation of their key bindings. But that is only one of many possible ways of activating clickable text.
There is a function, mouse-on-link-p, that determines if the given position is within clickable text, but there is no corresponding activation function.
Bob