Hosted annually in February, at the Irish Village, The Dubai annual Tennis Championship boasts prize money in excess of $1m and attracks most of the top 10 men and women players to the city. Tickets are becoming more difficult to access as the stadiums capacity is just over 5,000. These are sold online through time out tickets, normally a month before the tournament.
Tennis is a popular sport in Dubai, with lessons available from places like the aviation club which hosts 8 courts and is open to members and non members. See www.aviationclub.ae
The Dubai tennis academy at the American University offers lessons with internationally qualified coaches. See www.dubaitennisacademy.com
The same applies to The Emirates Tennis academy at Emirates Golf Club. See www.dubaigolf.com and follow the link to Emirates Golf club.
Many of the beach clubs like Jumeirah Beach Hotel have tennis facilities and run leagues which are a good opportunity to meet people when you arrive in Dubai. Most of these clubs also run lessons for juniors.