Definition of possessive | Bee Dictionary of English

n the case expressing ownership
a serving to express or indicate possession
possessive pronouns
s desirous of owning
small children are so possessive they will not let others play with their toys
s having or showing a desire to control or dominate
a possessive parent

A boy who has fallen in love with a local princess dives for pearls in a deep-sea grotto that is guarded by a possessive shark.
Yet despite his transgressions, Chan has never surrendered the love of his possessive admirers.
Readers are a very possessive bunch.

Father's Day: Tell him what he means to you - COLUMN
I don’t need to tell you that we, in the United States, will celebrate Fathers’ Day (yes, Fathers’, plural possessive). You already know that because we have been bombarded with ads for gifts for fathers. Frankly, do they really need more automatic screwdrivers, ties (Do they wear ties anymore?) and shaving lotion or Old Spice deodorant? I don’t think so, but that’s just my opinion.
June 13, 2013 - The Oakland Press
Dog kills boy who survived Oklahoma tornado
At the tender age of five, surviving a tornado a mile wide is, at the least, traumatizing. Being separated from mom and dad after that, and living in a strange house, is enough to make a little boy break down and cry. Through the eyes of a dog, possessive of its owner, a stranger in the house screaming at a family member can look like a threat that must be dealt with. The two scenarios cruelly ...
June 12, 2013 - KSAT San Antonio
OPINION: Father's Day: Tell him what he means to you
I don’t need to tell you that we, in the United States, will celebrate Fathers’ Day (yes, Fathers’, plural possessive). You already know that because we have been bombarded with ads for gifts for fathers. Frankly, do they really need more automatic screwdrivers, ties (Do they wear ties anymore?) and shaving lotion or Old Spice deodorant? I don’t think so, but that’s just my opinion.
June 11, 2013 - The Oakland Press

Cameron Diaz in The Gossip Girls (blog)
She also added a subtle jab at JT's ex Cameron Diaz, saying, "Jessica's really sweet. She's his age and isn't possessive. I think their personalities are a lot alike."
Glen Sather in ESPN
We had lost our zip at some point,Sather said. "We were a fast, puck-possessive hockey club that was determined and worked very hard and moved the puck well. We've gotten away from that and that's why we made the change."
Mark Hamill in Los Angeles Times
It wasn't like I declaimed one day 'I'm going to be a director,'Hamill said. "But I eventually realized I can become very possessive [with my work]. It's like having a child - if I get to act and not direct I might be banned from the set...