Should you tell the boss if you don't have enough work to do? May be the reorganisation has left you in a bit of a limbo, maybe your new boss doesn't know how best to use you or doesn't know much about what you and your team do. You could of course use this opportunity to spend more time with your team, take it in turn to shadow each of them for a day, move to weekly team meetings, offer more in-depth one to ones rather than the one hour once a month they are accustomed to. They may not welcome the extra attention after all their workload hasn't decreased. You could emphasis your corporate credentials by joining one of the many working groups maybe on the culture change, staff engagement, citizen empowerment, or next years budget strategy. But then previous experience of the equality and diversity group was that managers sent substitutes so every meeting half an hour was wasted bring them up to speed and nothing could ever be agreed as they had to report back to their manager first. You could fix up some joint team meetings with partner agencies but some of them are so dysfunctional that it's counter productive your team just end up resenting the time and feeling they have even less in common than they thought. You could work on your informal contacts both within the organisation and out side but you are the only one who seems to have the time and space everyone else seems to need 3 months notice for a diary date!
If you tell your boss you have some spare capacity one of two things is going to happen they are either going to overload you by delegating all the things they don't fancy doing, and of course you're not going to get any more money for the additional hassle or you're going to find your post at risk come the next round of budget cuts.
You could keep quiet, look busy, take a lunch hour, book some holidays and check out what your redundancy payout is likely to be.