Pet theory oddly has to take in male first (7)
I believe the answer is:
hamster
'pet' is the definition.
(I've seen this before)
'theory oddly has to take in male first' is the wordplay.
'oddly' means one should take alternating letters.
'to take in' means one lot of letters goes inside another.
'male' becomes 'm' (common abbreviation).
'first' means one lot of letters go next to another.
The alternating letters of 'theory' are 'ter'.
'has' going around 'm' is 'hams'.
'ter' put after 'hams' is 'HAMSTER'.
(Other definitions for hamster that I've seen before include "Rodent often kept as pet" , "Rodent with large cheek pouches" , "Animal" , "Pet rodent, may be golden" , "Kind of rodent with cheekpouches, often a pet" .)