Starts to like our groovy record (3)
I believe the answer is:
log
'record' is the definition.
(I know that log is a type of record)
'starts to like our groovy' is the wordplay.
'starts to' says to take the initial letters.
The first letters of 'like our groovy' is 'LOG'.
(Other definitions for log that I've seen before include "fuel consumed" , "Diary kept by ship's captain" , "Formal record" , "Listing" , "Written account of a voyage" .)