4 added 96 characters in body
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Perl 6, 34 32 3230 bytes

Thanks to nwellnhof for -2 bytes through the use of the o operator to combine functions

{substr S/.//}o{base( :36(1~$_)+1: 36),1}

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Function that converts the argument to base 36, adds 1, converts back and then formats it. Now uses the same tactic as Adnan's answer to preserve the leading zeroes.

Perl 6, 34 32 bytes

{substr base(:36(1~$_)+1: 36),1}

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Function that converts the argument to base 36, adds 1, converts back and then formats it. Now uses the same tactic as Adnan's answer to preserve the leading zeroes.

Perl 6, 34 32 30 bytes

Thanks to nwellnhof for -2 bytes through the use of the o operator to combine functions

{S/.//}o{base :36(1~$_)+1: 36}

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Function that converts the argument to base 36, adds 1, converts back and then formats it. Now uses the same tactic as Adnan's answer to preserve the leading zeroes.

3 -2
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Perl 6, 3434 32 bytes

{substr base(:36($_1~$_)+1: 36).fmt("%010s"),1}

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Function that converts the argument to base 36, adds 1, converts back and then formats it. Now uses the same tactic as Adnan's answer to preserve the leading zeroes.

Perl 6, 34 bytes

{base(:36($_)+1: 36).fmt("%010s")}

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Function that converts the argument to base 36, adds 1, converts back and then formats it.

Perl 6, 34 32 bytes

{substr base(:36(1~$_)+1: 36),1}

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Function that converts the argument to base 36, adds 1, converts back and then formats it. Now uses the same tactic as Adnan's answer to preserve the leading zeroes.

2 -2 bytes
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Perl 6, 3634 bytes

{base(:36(~$_$_)+1).base(: 36).fmt("%010s")}

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Function that converts the argument to base 36, adds 1, converts back and then formats it.

Perl 6, 36 bytes

{(:36(~$_)+1).base(36).fmt("%010s")}

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Function that converts the argument to base 36, adds 1, converts back and then formats it.

Perl 6, 34 bytes

{base(:36($_)+1: 36).fmt("%010s")}

Try it online!

Function that converts the argument to base 36, adds 1, converts back and then formats it.

1
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