Leaning on grandfather, say, with a deadline (7,3,5)
I believe the answer is:
against the clock
'with a deadline' is the definition.
(I've seen this in another clue)
'leaning on grandfather' is the wordplay.
'leaning on' becomes 'against' (I've seen this in another clue).
'grandfather' becomes 'theclock' (I can't justify this - if you can you should give a lot more credence to this answer).
'against'+'theclock'='AGAINST THE CLOCK'
'say' acts as a link.
Can you help me to learn more?
(Other definitions for against the clock that I've seen before include "under pressure" , "in a desperate hurry?" , "subject to time constraints" , "How hands may be viewed" .)