How to find the overlap between 2 sequences, and return it

Have a look at the difflib library and more precisely at find_longest_match():

import difflib

def get_overlap(s1, s2):
    s = difflib.SequenceMatcher(None, s1, s2)
    pos_a, pos_b, size = s.find_longest_match(0, len(s1), 0, len(s2)) 
    return s1[pos_a:pos_a+size]

s1 = "CGATTCCAGGCTCCCCACGGGGTACCCATAACTTGACAGTAGATCTC"
s2 = "GGCTCCCCACGGGGTACCCATAACTTGACAGTAGATCTCGTCCAGACCCCTAGC"

print(get_overlap(s1, s2)) # GGCTCCCCACGGGGTACCCATAACTTGACAGTAGATCTC

You could use difflib.SequenceMatcher:

d = difflib.SequenceMatcher(None,s1,s2)
>>> match = max(d.get_matching_blocks(),key=lambda x:x[2])
>>> match
Match(a=8, b=0, size=39)
>>> i,j,k = match
>>> d.a[i:i+k]
'GGCTCCCCACGGGGTACCCATAACTTGACAGTAGATCTC'
>>> d.a[i:i+k] == d.b[j:j+k]
True
>>> d.a == s1
True
>>> d.b == s2
True