Bank simply ignoring me (4)
I believe the answer is:
rely
'bank' is the definition.
(thesaurus)
'simply ignoring me' is the wordplay.
'simply' becomes 'merely' ('merely' can be a synonym of 'simply').
'ignoring' indicates named letters should be taken away.
'merely' with 'me' taken away is 'RELY'.
(Other definitions for rely that I've seen before include "All the letters" , "Depend (upon)" , "Trust, depend" , "Old rally" , "City with cathedral" .)