Phew, there's many ways to tackle this, and it comes down to "how gritty" you want the game to be.
The extreme version would be that any clothing not discarded before the act would get ripped apart, whilst the shapeshifter is screaming in pain as his bones and flesh transform into a new image, complete with nasty cracking sounds and a rather ... disorienting effect on the caster that would last for a moment even after the transformation is completed.
The easiest way, on the other hand, is the caster switching into a new shape with a snap of his fingers, any clothing transforming with him - and reappearing when he changes back. Ironically, for all the darkness the fantasy in Dragon Age has, this seems to be how it is done in the computer games, including the Sacred Ashes
trailer (watch Morrigan at 02:10).
Interesting detail: she at least drops her staff before switching into spider-mode.
Or perhaps - to offer a compromise between these two options - how about making it so that only things that have been "alive" at some point (wool, wood, leather, bone) would transform with the caster, but anything else (metal, stone, crystal) not? For some reason, this feels much easier to imagine than, say, a slab of steel warping itself into the caster's new shape.
This would also encourage shapeshifters to keep their abilities in mind when purchasing gear, preferring "suitable" equipment such as knives made from bone or jewelry made from wood and amber instead of the usual steel and gold.