Hi,
I used to pronounce the a's in those kinds of words the same as the "a" in "cat", /æ/ - /kæt/ (IPA).
Now I'm trying to change that, and I always try to pronounce those a's followed by r's as in "air", /er/ (IPA).
So I used to say "clarity" as /klærəti/ (precise IPA transcription: /klæɹəɾi/)
and now I say "cl-air-uh-ti", /klerəti/ (precise IPA transcription: /kleɹəɾi/)
You can hear "clarity" as "cl-air-uh-ti" here:
http://www.merriam-webster.com/dictionary/clarity (click on the red little speaker)
I don't know what's the difference, but maybe /klærəti/ is more of a feature of the English spoken on the East Coast of the USA (and maybe British English, according to my dictionaries, but I really don't know, I'm really not an expert in British English).