Bridge player initially breaking into clubs — I say, hearts overlooked! (10)

'bridge' is the definition.
(the bridge of a stringed instrument)

'clubs i say hearts overlooked' is the wordplay.
'clubs' becomes 'pontic' (I can't justify this - if you can you should give a lot more credence to this answer).
'i say' becomes 'hello' (both are expressions of surprise).
'hearts' becomes 'h' (abbreviation used in card games e.g. bridge).
'overlooked' indicates named letters should be taken away.
'hello' with 'h' taken away is 'ello'.
'pontic'+'ello'='PONTICELLO'

'player initially breaking into' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.