Hazy sun out perhaps around the end of June (7)
I believe the answer is:
tenuous
'hazy' is the definition.
(thesaurus)
'sun out perhaps around the end of june' is the wordplay.
'perhaps' is an anagram indicator.
'around' is an insertion indicator.
'the end of' suggests the final letters.
The last letter of 'june' is 'e'.
'sun'+'out'='sunout'
'sunout' anagrammed gives 'tnuous'.
'tnuous' placed around 'e' is 'TENUOUS'.
(Other definitions for tenuous that I've seen before include "Flimsy, thin" , "Very slight, insubstantial" , "Very thin in form, having little validity" , "Very slight (connection)" , "Sketchy" .)