They imagine a lot of journalists will accept offer (10)

'they imagine' is the definition.
(people who imagine)

'a lot of journalists will accept offer' is the wordplay.
'a lot of' means to remove the last letter (I've seen 'lots of' mean this (the majority of the word)).
'journalists' becomes 'press' (I've seen this before).
'will accept' indicates putting letters inside.
'offer' becomes 'tender' (tender is a kind of offer).
'press' with its last letter taken away is 'pres'.
'pres' going around 'tender' is 'PRETENDERS'.