Anxiety shown by member touring LA (5)
I believe the answer is:
alarm
'anxiety' is the definition.
(thesaurus)
'by member touring la' is the wordplay.
'by' means one lot of letters go next to another.
'member' becomes 'arm' (member can mean a limb).
'touring' indicates anagramming the letters (touring can mean moving around).
'la' is an anagram of 'al'.
'arm' after 'al' is 'ALARM'.
'shown' is the link.
(Other definitions for alarm that I've seen before include "Warning sound/device" , "Flap" , "Great concern" , "Wake-up call?" , "Warning of danger" .)