There are a number of sporting clubs and community organisations in Exmouth. Details available at this link:
https://www.exmouth.wa.gov.au/listings/sporting-clubs-and-community-organisations/sporting-clubs
There is an outdoor 50m swimming pool in the centre of town which is managed by the Shire.
Other fitness:
Ningaloo Reef Gym: https://www.facebook.com/profile.php?id=100070301631466
Inhala Yoga Studio
Julianne Armer Pilates
Ningaloo Pure Moves
Element Movement: https://elementmovement.com.au/