Muggles, muggles everywhere! Let's face it, this is a really busy location. It's right by a busy crossroads, next to a foot and cycle path, in front of the swimming pool, fire station and police station. You will be waiting a long time for a quiet moment to climb ths tree, so you might as well just bite the bullet and go for it.
The cache is a 35mm film conatiner, camouflaged, cable tied to a branch. You can see it from the ground if you know where to look. Most of the Ascension series caches are quite low in the tree. This one is near the top. The branches are thin up there, be careful!
Parker's Piece itself was obtained by the city from Trinity College some centuries ago. It has a claim to fame of being the birthplace of association football, and is also host to a street lamp which has its own Wikipedia page; (and also a multi cache by my partner in crime, The Local Echo).
Happy climbing!