Hello
The cut off for admission in any of the National Law Universities through CLAT in the previous year was a rank in the range of 1600 for the general category. Considering that your rank is 6573, your chances are less.

Usually there are vacancies in the lower NLUs as people leave their seats for other colleges. You might have less chances even then. Usually a rank under 3000 is safe for admission under Vacanies.

Though chances are less i would still suggest you to apply for it as firstly there is no harm in trying and also because this year there have been quite a large number of vacancies among different NLUs.
Along with HPNLU other NLus like NLu raipur etc also have vacancies you can check their official websites too.
But along with it i would also suggest you to not only rely on this and also find another back up option in case you don't get selected because  your chances are quite less.
Other than colleges with their own entrances, There are various Private Colleges that accept CLAT scores other than the National Law Universities.

NLU Odisha

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NLU Delhi

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NLU Shimla (HPNLU)

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