Encountered rising annoyance in storm (7)
I believe the answer is:
tempest
'storm' is the definition.
(tempest is a kind of storm)
'encountered rising annoyance' is the wordplay.
'encountered' becomes 'met' ('meet' can be a synonym of 'encounter').
'rising' says the letters should be written in reverse (going up in a down clue).
'annoyance' becomes 'pest' (I've seen this before).
'met' backwards is 'tem'.
'tem'+'pest'='TEMPEST'
'in' is the link.
(Other definitions for tempest that I've seen before include "Violent wind storm" , "Cyclone" , "An angry storm as in Shakespeare play" , "Pets met in violent storm" , "violent uproar" .)