Eat eagerly, like at home (3,2)
I believe the answer is:
dig in
'eat eagerly' is the definition.
'like at home' is the wordplay.
'like' becomes 'dig' (I've seen this in other clues).
'at home' becomes 'in' ('in' can be similar in meaning to 'at home').
'dig'+'in'='DIG IN'
(Other definitions for dig in that I've seen before include "Start to scoff" , "Begin eating heartily" , "Start to eat" , "Start eating (informal)" , "prepare trench" .)