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