Sticky mess of scrambled egg around mid-June (5)
I believe the answer is:
gunge
'sticky mess' is the definition.
(I've seen this before)
'scrambled egg around mid-june' is the wordplay.
'scrambled' is an anagram indicator.
'around' means one lot of letters goes inside another.
'mid' says to take the centre (mid- can mean the middle of something).
The middle letters of 'june' are 'un'.
'egg' anagrammed gives 'gge'.
'gge' placed around 'un' is 'GUNGE'.
'of' is the link.
(Other definitions for gunge that I've seen before include "Sticky stuff (colloq.)" , "Unpleasant thick substance" , "Unpleasantly sticky or viscous material" , "Unpleasant sticky material" , "Dirty substance" .)