Presuming this q is off the back of the recent Edinburgh case?
The FAQs section of the FTT website states that, re awarding compensation to parties,
"No, the tribunal have no powers to award compensation to any party in an application.
However, the First-tier Tribunal has the power to award expenses against a party where that party through unreasonable behaviour in the conduct of the case has put any other party to unnecessary or unreasonable expense. Exercise of this power is not linked to the outcome of the case."
So it looks like, in exceptional cases, it can award expenses but the general premise is that this shouldn’t be the case.
For more information on raising an FTT action, Shelter Scotland has a section on their ‘Get Advice’ pages which might be useful.