Don't go without a pen (3)
I believe the answer is:
sty
'pen' is the definition.
(both can mean an animal enclosure)
'don't go without a' is the wordplay.
'don't go' becomes 'stay' (I've seen this in another clue).
'without' suggests deleting specific letters.
'stay' with 'a' taken away is 'STY'.
(Other definitions for sty that I've seen before include "Pig-house" , "Animal pen" , "Pig house" , "Hog house" , "Pig pen" .)