Measure of frequency of period pains reported (5)
I believe the answer is:
hertz
'measure of frequency' is the definition.
(unit of frequency)
'pains reported' is the wordplay.
'pains' becomes 'hurts' (hurt is a kind of pain).
'reported' indicates a 'sounds like' (homophone) clue.
'hurts' sounds like 'HERTZ'.
'of period' is the link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for hertz that I've seen before include "A measure of frequency" , "Cycles per second unit" , "Unit of frequency - German physicist, d. 1894" .)