Remain longer than old occasionally rusty cable (7)
I believe the answer is:
outstay
'remain longer than' is the definition.
(I've seen this before)
'old occasionally rusty cable' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'occasionally' indicates alternate letters.
'cable' becomes 'stay' (I can't justify this - if you can you should give a lot more credence to this answer).
The alternating letters of 'rusty' are 'ut'.
'o'+'ut'+'stay'='OUTSTAY'
Can you help me to learn more?
(Other definitions for outstay that I've seen before include "remain too long" , "abuse welcome" , "Remain beyond" , "Remain longer than" , "Show more stamina than others" .)