Steadier lassoes left by one more likely to snap (7)

'more likely to snap' is the definition.
(surly can mean bad-tempered)

'steadier lassoes left by one' is the wordplay.
'steadier' becomes 'surer' (sure can mean steady or firm).
'lassoes' indicates putting letters inside (inserted letters are lassoed or caught).
'left by' becomes 'l' (I've seen this in other clues).
'one' becomes 'I' (Roman numeral).
'l'+'i'='li'
'surer' going around 'li' is 'SURLIER'.