Baby ape running inside vessel (6)
I believe the answer is:
teapot
'vessel' is the definition.
(teapot is a kind of vessel)
'baby ape running inside' is the wordplay.
'baby' becomes 'tot' (I've seen this in another clue).
'running' indicates an anagram (the letters run around to different places).
'inside' means one lot of letters goes inside another.
'ape' is an anagram of 'eap'.
'tot' going around 'eap' is 'TEAPOT'.
(Other definitions for teapot that I've seen before include "Spouted holder" , "Vessel for brewing leaves" , "Kitchen vessel with handle, lid and spout" , "Spouted vessel" , "where one might find leaves" .)