Taking place annually at the Aviation Club Tennis Centre, The Dubai Tennis Championship boasts prize money in excess of $1m and attracts the top 10 men and women players to the city. This event is hugely popular and tickets are sought after several months in advance.
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.