Here are two steps you should take after having a new roof fitted.
Get gutter guards installed
One of the best investments you can make after your roofer has fitted the new roof is a set of gutter guards. These usually feature a sturdy, gutter-shaped mesh that is designed to be placed on top of a building's gutters.
A gutter guard can stop the usual debris that clogs up gutters (i.e., bird droppings, leaves, dirt, etc.) from landing in the gutters; this then allows whatever rainwater that falls into the gutters (through the guard's fine mesh) to flow steadily through the gutters and exit through the downpipes, without overflowing.
This could not only keep your gutters in good condition but could also help to maintain your new roof's lifespan. This is because when gutters get clogged up and aren't immediately unclogged, the stagnant rainwater that's in them starts to overflow and saturate the low-positioned roof tiles that sit just above the gutters. This constant saturation can cause moss growth and speed up the tiles' deterioration. As such, by using guards that prevent clogged gutters, you should be able to protect this section of your new roof from damage.
Check the roof and gutters for leaves, snow and general debris regularly
After you (or your roofer) fit the gutter guards, you should start checking both the roof and the gutter guards for snow, leaves, and general debris on a regular basis. There are several reasons why it's worth doing this. Firstly, whilst a gutter guard will prevent blockages in the gutter it's placed on top of, the debris that lands on this mesh will need to be periodically swept off, to ensure that it doesn't form an impenetrable layer over the guard (as this layer would stop rainwater from getting into the gutter and flowing away from the building, via its pipes, and thus cause the roof damage described above).
Secondly, checking the roof itself for debris and, if possible, sweeping this debris off the roof (by using an extendable brush or having your roofer climb up on a ladder to remove it for you) will stop this debris from, for example, saturating the roof tiles for too long (which can happen with both damp, dead leaves in the autumn and with snow in the winter) or from putting too much strain on the roof (which can occur when large amounts of snow are left on a roof surface for days or weeks at a time). Doing these checks regularly should protect your new roof and ensure that the gutter guards continue to function in the way they're supposed to.