Resignation statement in University Times, it being all over (8)
I believe the answer is:
ubiquity
'being all over' is the definition.
(ubiquity is the quality of being everywhere)
'resignation statement in university times' is the wordplay.
'resignation statement' becomes 'iquit' (the phrase 'I quit' is used to resign a post).
'in' indicates putting letters inside.
'university' becomes 'u'.
'times' becomes 'by' (I've seen this in other clues).
'u'+'by'='uby'
'iquit' inserted within 'uby' is 'UBIQUITY'.
'it' is the link.
This may not be right. It may be part of another bit of the clue.
(Other definitions for ubiquity that I've seen before include "Existence everywhere at the same time" , "appearing everywhere" , "Omnipresence" , "Universality" , "State of being (or seeming to be) everywhere at once" .)