you can set the input record separator to \n\n to read the paragraph format you have there. then the default sort will work, if the prefix is the same on every line.

#!perl

use strict; use warnings;

my @data;
{
    local $/ = "\n\n";
    @data = <DATA>;
}

my @sorted = sort @data;
print @sorted;

__DATA__
>ENSP00000314624
GCACAATGGTAGAGGCAGATCATCC

>ENSP00000347089
ATGGATTGCTGTGCCTCTCGAGGCT

>ENSP00000301587
TGACCCACTTCCGTTACTTGCTGCG
[download]

produces

>ENSP00000301587
TGACCCACTTCCGTTACTTGCTGCG

>ENSP00000314624
GCACAATGGTAGAGGCAGATCATCC

>ENSP00000347089
ATGGATTGCTGTGCCTCTCGAGGCT