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Presuming you mean gutter covers, should be installed at same time if coming from same company - there are some companies who only do gutter covers so would be done after the gutters in that case, but you need to coordinate between them to be sure setting height of the gutters suits the cover design.(Not that I am recommending covers - I have never seen a brand that is worth the hassle).
Drip edge would go in normally during a reroof, but it is commonly possible to do so after the fact with some hassle - has to be in BEFORE the gutters or the covers in many cases because of tight conditions with the gutter there - and almost always the covers have to come off (or be off) to install the drip edge. I note you said the current gutters do not have a drip edge - you do realize the drip edge goes onthe roof edge up under the shingles and water barrier, right - not on the gutters themselves. A totally separate piece of metal, tucked under the roofing/water barrier, and overhanging down into the gutter a bit ideally to minimize backsplash or wind blowing it onto the fascia board, though most gutter covers prevent it doing that so you end up with fascia and trim and sheathing edge water damage because of the guttear cover.

Gutter apron is installed with initial roof installation.

It must be installed before guttering or damage to the fascia may occur.

See my website for a gutter cover that comes with 100% money back factory warranty if they ever clog.

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Source: www.heartlandmastershield,com