Заменить:
for department in containers:
if(department.find('a')):
data['Department'].append(department.find('a', {'class': 'speciality'}).text)
data['Conditions'].append(department.find('div', {'class': 'links'}).text)[0:]
С:
for department in containers:
if(department.find('a')):
data['Department'].append(department.find('a', {'class': 'speciality'}).text)
links = department.find('div', {'class': 'links'})
for link in links.find_all("a"):
data['Conditions'].append(link.get_text())