Use .find()or .find_all()to select the element (s) that has an attribute hrefand a class attribute Unique_Class_Name. Then iterate over the elements and get access to the attribute value href:
soup = BeautifulSoup(html)
anchors = soup.find_all('a', {'class': 'Unique_Class_Name', 'href': True})
for anchor in anchors:
print (anchor['href'])
CSS .select():
soup = BeautifulSoup(html)
for anchor in soup.select('a.Unique_Class_Name'):
if anchor.has_attr('href'):
print (anchor['href'])