The wet patch on your ceiling is almost never under the hole. Here is the method we use, which you can do yourself.
The single most useful thing in roofing costs nothing and is not a skill: a hose, a helper and an hour, working from the bottom of the slope upwards.
Water does not fall straight through a roof. It gets in, runs along the underside of a sheet or along a purlin, and leaves at the first place it can. Three metres between the entry and the ceiling stain is ordinary, and on a shallow roof it can be much more. So the wet patch tells you almost nothing about where to look, and this is why so many roofs here get a new sheet fitted over a hole that was never the problem.
The method. One person inside with a torch, looking at the underside. One person outside with a hose running gently, not at pressure, because pressure pushes water where rain never would and will show you a leak that does not exist in real weather.
Start at the lowest edge, wet one section for two or three minutes, and wait. Wait longer than feels necessary; a slow path can take five minutes to appear. Then move a little way up the slope and repeat. The first place water appears inside is below the entry point, and you have now bracketed it to within a metre.
What you will usually find at that point is one of four things. A fixing that has backed out, because metal moves a surprising distance in heat and screws walk out over years. A lap that has lifted, usually on the windward side. Ridge flashing that was never sealed, only overlapped. Or, most often of all and the cheapest to fix, a gutter full enough that water backs up under the bottom sheet.
All four are a morning's work. None of them is a new roof. If you want to do the hose test yourself before calling anybody, do, and tell us what you found. We would far rather arrive knowing.