A danger out east at this time of the year (5)
I believe the answer is:
april
'this time of the year' is the definition.
(I've seen this before)
'a danger out east' is the wordplay.
'danger' becomes 'peril' (peril is a kind of danger).
'out' is a deletion indicator.
'east' becomes 'e' (abbreviation).
'peril' with 'e' taken away is 'pril'.
'a'+'pril'='APRIL'
'at' is the link.
(Other definitions for april that I've seen before include "Reputedly showery month" , "days on end" , "Eliot's 'cruellest month'" , "period of time" , "4th month" .)