Inertial containment fusion relies on firing a laser at an extremely precisely machined piece of heavy metal (called a hohlraum), heating it until it emits X-Rays, and using the X-Rays to create 2 implosion shockwaves in a tiny pellet of tritium + deuterium that have to meet in the dead center, so that where they meet they can start a fusion reaction, and ideally have the fusion reaction consume the whole pellet before the shockwaves dissipate enough to stop confining the plasma. A few microseconds after the laser blast, you get a puff of helium (+hydrogen if the reaction wasn't complete) and a mangled piece of metal, and some heat that in principle you could capture somehow, though no one has yet tried. Then, you throw away the now useless hohlraum, get a new one and a new pellet and you fire again for another little burst of energy, over and over.

The hohlraum is the biggest problem here: the level of precision needed to achieve the exact geometry inside the pellet to actually ignite a plasma means that every hohlraum is (a) extraordinarily expensive (currently in the millions of dollars range), and (b) entirely useless after a single shot - while continuous operation for a 1500 MW plant is estimated to require ~20 hohlraums/second).

For a spaceship design, this would mean that your engine would have to include a smelter and high-precision machining bay to constantly create new micrometer-smooth hohlraums from spent ones. Not even close to a promising technology.