He designed spa resorts, showing stubborn nature (13)
I believe the answer is:
pigheadedness
'stubborn nature' is the definition.
(pigheaded can mean stubborn or obstinate)
'he designed spa resorts' is the wordplay.
'resorts' is an anagram indicator.
'he'+'designed'+'spa'='hedesignedspa'
'hedesignedspa' anagrammed gives 'PIGHEADEDNESS'.
'showing' acts as a link.
(Other definitions for pigheadedness that I've seen before include "Obstinacy" , "Stupidly obstinate quality" .)