You can get angler gloves from Fishing Trawler. It is a very rare drop. It is an Experience-boosting set for the fishing skill. The skilling outfit is part of the Angular's outfit. You can get the other pieces of the outfit by Arial Fishing. However, that means you need to complete quests to access Great Kourend/Zeah. You do get Hunter/Fishing XP there which makes training those two skills easy.

Angler's outfit

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