The problem about technetium - variable and peevish (6)
I believe the answer is:
tetchy
'peevish' is the definition.
(I know that peevish can be written as tetchy)
'the problem about technetium variable' is the wordplay.
'problem' indicates an anagram.
'about' indicates putting letters inside.
'technetium' becomes 'Tc' (Tc is the chemical symbol for technetium).
'variable' becomes 'y' (algebra).
'the' is an anagram of 'teh'.
'teh' placed around 'tc' is 'tetch'.
'tetch'+'y'='TETCHY'
'and' is the link.
(Other definitions for tetchy that I've seen before include "Bad-tempered" , "Ratty" , "liable to blow a fuse" , "Informally irritable" , "Easily irritated or annoyed, narky" .)