Tom, put these gloves on.
Tip: You can omit particle を in a very casual conversation/online chat. But the whole sentence is mess. If you politely ask Tom to do so by saying ～してください (please), I don’t recommend to drop を. Also, you need to add さん for Tom when it is followed by ～ください.
トムさん、手袋をしてください。(like Tom is a client and a visitor to our factory and the host politely asks Tom as a standard safety measure.)
トム、手袋して！ (the speaker and Tom are friends, colleagues or family members)
are more natural.