That report says the bill is only days or weeks away from becoming law. That isn't true, it is still being debated in the Commons and still has to progress through the Lords before being ratified. Months away at best.
It proposes that primates cannot be kept without a licence. That can only be a good thing, primates are not ideal pets and are difficult to keep.
It also proposes stronger penalties for owners of dogs that attack livestock.
Bans exports of livestock for slaughter.
Interestingly the UK exports the fewest number of livestock in Europe and our biggest export is horses, presumably for horsemeat.
Creates the offence of 'dognapping', currently it is treated as theft.
Applies restrictions on the import of 'certain dogs, cats and ferrets' - it seems to aim to limit the import of 'rescue dogs' from Eastern Europe and other countries but I could be wrong. If any is interested, I would appreciate clarification.
Reclassification of zoos.
It is not a major overhaul of the law and I can't see why Truss would oppose it. Maybe she is a major exporter of horses and chickens and has a houseful of spider monkeys.