imitate
verb
1 it was quite acceptable for artists to imitate other artists:
emulate, copy, take as a model, model oneself on, take as a pattern, pattern oneself on/after, follow the example of, take as an example, take as a role model, take after, follow, follow in someone's steps/footsteps;
echo, parrot;
follow suit, take a leaf out of someone's book;
informal rip off.
2 he was a splendid mimic, and loved to imitate Winston Churchill:
mimic, do an impression of, impersonate, ape;
parody, caricature, burlesque, travesty, mock;
masquerade as, pose as, pass oneself off as;
informal take off, send up, spoof, do;
North American, informal make like;
archaic monkey;
rare personate.