is the grammar correct?

using *at First* is not grammatically wrong, but in your situation, it will be better to use *Firstly*. Because you are describing some sort of procedure, so usually you will use words like *firstly*, *secondly*, *finally* etc.

*...are qualified to job requirment..* is grammatically incorrect. One would not use *qualified to*. should be *qualified for* something.
In your case, I think it would be better if you say *the HR manager identifies / checks if / whether the applications meet / match with / satisfy the job requirement in that department and supervisors' expectation or not.*

*...are any changes about the job description* is not incorrect, but it should be *changes to* instead of *changes about*.

*s* is missing from *tell*. *the line manager tells* and *line managers tell*.

*tells HR about the changed information* is correct, but you may consider using *tells HR of the changes made*.

*...so as to select the best people* is grammatically correct, but you may consider using *so as to select the most suitable candidates for the job*.


Hope the above can be of help!

2006-12-10 14:05:40 補充：
At the very beginning, you may even using *First* instead of *at first* or *firstly*.

The HR manager should first check the applications to see if they satisfied both the job requirement needed for that department and the supervisors' expectation. If there are any changes to the job description, the line manager should tell the HR immediately about the changed information so that the best people can be selected.