Something like below should do the trick,
curl -sk -u useraccount -H "Content-Type: application/json" -X PATCH https://hostname/mgmt/tm/auth/user/useraccount -d '{ "password": "newpassword" }'
Once above is it will prompt for existing password and the change will reflect. The user will have the newpassword set as password.
If you'd need you can send the existing password in the query too.
curl -sk -u useraccount:oldpassword -H "Content-Type: application/json" -X PATCH https://hostname/mgmt/tm/auth/user/useraccount -d '{ "password": "newpassword" }'
Hope this helps.