Today, disheartened depositor admitted to strain in chilly bank (9)
I believe the answer is:
snowdrift
'chilly bank' is the definition.
(a snowdrift is a bank or heap of snow)
'today disheartened depositor admitted to strain' is the wordplay.
'today' becomes 'now' (synonyms).
'disheartened' says to hollow out the word (remove centre letters).
'admitted to' means one lot of letters goes inside another.
'strain' becomes 'sift' (synonyms).
'depositor' with its middle removed is 'dr'.
'now'+'dr'='nowdr'
'nowdr' inserted inside 'sift' is 'SNOWDRIFT'.
'in' acts as a link.
(Other definitions for snowdrift that I've seen before include "Midwinter may show one" , "Wintry accumulation" , "evidence of wintry weather" , "Wintry feature" , "Winter problem" .)