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 before).
'running' indicates anagramming the letters (the letters run around to different places).
'inside' indicates putting letters inside.
'ape' anagrammed gives 'eap'.
'tot' placed 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" .)