A new set of brake pads usually comes with fresh clips and hardware, and it is tempting to skip them and reuse the old parts. In most cases you should not - worn hardware causes noise and uneven wear. Here is the reasoning.
Clips lose their spring
The abutment clips and anti-rattle springs hold the pads with light tension. Over years of heat cycles they lose their springiness and can corrode - see brake hardware clips. Reused tired clips let pads rattle or bind, which is a top cause of brake noise; see why brakes squeak.
Rust changes the fit
Corrosion builds up under old clips and can keep a new pad from sliding freely in the bracket - a stuck pad drags and wears unevenly, and can even keep a new pad from seating; see new pad won't fit. Fresh clips restore the clean, correct slot.
When reuse is okay
If the existing hardware is genuinely clean, rust-free, and still springy - and no new clips came in the box - reuse can be acceptable. But if new clips are included, use them; they are cheap insurance against noise.
Best practice
Replace clips and hardware with every pad change, grease the contact points lightly, and torque everything correctly. Pair quality pads with fresh hardware for the quietest result.