Clue: Might run into nasty gents on outskirts of Teignmouth (8)
Answer: STRENGTH
Explanation: Definition: Might
 R(abbrev. for "run", in cricket scores) **contained in**(into) **anagram of**(nasty) GENTS **placed above**(on, in a down clue) **1st and last letters of**(outskirts of) "Teignmouth".