{
    local $/ = 'Query= ';

    while (<$filehandle>) {
        print "$1\t$2" if / \A (\S+) .*? ^ > (\S+) /msx;
    }
}

##</code><code>##

#!/usr/bin/env perl -l

use strict;
use warnings;

{
    local $/ = 'Query= ';

    while (<DATA>) {
        print "$1\t$2" if / \A (\S+) .*? ^ > (\S+) /msx;
    }
}

__DATA__

Query= sp|P30443|1A01_HUMAN HLA class I histocompatibility antigen,
A-1 alpha chain OS=Homo sapiens GN=HLA-A PE=1 SV=1
         (365 letters)

...
>tr|G1KTN1|G1KTN1_ANOCA Uncharacterized protein OS=Anolis
           carolinensis PE=3 SV=2
          Length = 358
...
>tr|L7MZX2|L7MZX2_ANOCA Uncharacterized protein OS=Anolis
           carolinensis GN=LOC100559978 PE=3 SV=1
          Length = 364
...

Query= Xsp|P30443|1A01_HUMAN HLA class I histocompatibility antigen,
A-1 alpha chain OS=Homo sapiens GN=HLA-A PE=1 SV=1
         (365 letters)

...
>Xtr|G1KTN1|G1KTN1_ANOCA Uncharacterized protein OS=Anolis
           carolinensis PE=3 SV=2
          Length = 358
...
>Xtr|L7MZX2|L7MZX2_ANOCA Uncharacterized protein OS=Anolis
           carolinensis GN=LOC100559978 PE=3 SV=1
          Length = 364
...


##</code><code>##

sp|P30443|1A01_HUMAN    tr|G1KTN1|G1KTN1_ANOCA
Xsp|P30443|1A01_HUMAN   Xtr|G1KTN1|G1KTN1_ANOCA