How do i run a minecraft datapack function when a player has a specific item in their inventory? (minecraft 1.15)

You can store the result of a command with /execute store. In this case:

/execute as @a store result score @s gold run clear @s gold_ingot{coin:1}

Then you can use that score for whatever you want. In this case you're just interested in whether it's 1 or more:

/execute as @a if score @s gold matches 1.. run <command>

As a nice side effect, this also runs the function as every player who matches that condition. If you don't want that, use /execute if entity @a[scores={gold=1..}] run <command> instead.

Also, if you just want to check whether someone has an item (or how much of it), without actually taking it away, use the /clear command with a count of 0.