Note the cat (from the quest where you rescue the woman's black panther) has no highlighted movement locations.  I see no spell effects on the cat (look at her card below to verify), let alone anything that would preclude moving.  The entire battle cat could not move.  Cat's turn came up normally, but each time, even with open adjacent tiles, cat could not move.

As cat has no items/spells/skills, I could not test if she could execute any actions.

All other units in this tactical battle moved normally.  Other units could move into the open tiles the cat could not enter.

The cat moves normally in every non-city tactical battle.  Cat has not been in a second city battle to test if this would recur.

Note: in this city tactical battle I had 7 city defender militia units (plus the normal 1 city defender archer) -- see my other bug post "[Bug 0.51] Reloading a save increments 2 city defender militia".  Is it possible the cat was placed on an invalid tile (because of the abnormal number of city defender militia?) and that's why she can't move?