Intrude, as menu inside has cold fish (8)
I believe the answer is:
encroach
'intrude' is the definition.
(thesaurus)
'menu inside has cold fish' is the wordplay.
'inside' says to take the centre.
'has' says to put letters next to each other.
'cold' becomes 'c' (eg on taps).
'fish' becomes 'roach' (roach is a kind of fish**).
The central letters of 'menu' are 'en'.
'en'+'c'+'roach'='ENCROACH'
'as' is the link.
(Other definitions for encroach that I've seen before include "Gradually intrude (on person's area)" , "Tread on someone's toes" , "Advance beyond proper limit" , "Advance gradually (beyond expected limits)" , "Gradually intrude (upon another's space)" .)