The 2006 Asian Games marked Jasim's breakthrough as a senior athlete. Although she was beaten by Kayoko Fukushi in the 10,000 m, she finished ahead of Hiromi Ominami to take the silver medal in a national record time of 32:17.14 minutes. She was part of a Bahraini medal sweep at the 2007 Asian Cross Country Championships, finishing second to her teammate Maryam Yusuf Jamal. At the Arab Athletics Championships in May she was second in the 5000 m and defended her half marathon title. She ran a 3000 m personal best of 9:14.30 minutes at the Hanžeković Memorial before going on to a long-distance double at the 2007 Asian Athletics Championships, going unchallenged in weak women's fields. Later in the season she was third in the 5000 m at the 2007 Military World Games and won the half marathon at the 2007 Pan Arab Games. She also set a half marathon best of 71:52 minutes in a second-place performance at the Route du Vin Half Marathon.