Smiled when the spider got me agitated (8)
I believe the answer is:
Here is my best explanation:
'smiled' is the definition.
(simpering is a kind of smiling)
'the spider got me agitated' is the wordplay.
'got' means one lot of letters go next to another.
'agitated' is an anagram indicator.
'spiderme' with letters rearranged gives 'SIMPERED'.
'when' acts as a link.
(Other definitions for simpered that I've seen before include "Smiled stupidly", "Smiled in affected way" and "made with mince".)