The side-form dog radical (a contracted 犬) is used for animals broadly, not just canines. It marks 猿 as a wild creature and groups it with 猴, 狼, 狮 - the four-legged-mammal family rendered with this slanting beast radical on the left.
Supplies the sound yuán unchanged. It heads a tight phonetic series with 园, 远, 援 and 辕 that all share this stem. The robe meaning is incidental - readers use 袁 here purely as a sound clue for the ape.
