As @DSM points out, you can do this more directly using the vectorised string methods:
df['Date'].str[-4:].astype(int)
Or using extract (assuming there is only one set of digits of length 4 somewhere in each string):
df['Date'].str.extract('(?P<year>\d{4})').astype(int)
An alternative slightly more flexible way, might be to use apply (or equivalently map) to do this:
df['Date'] = df['Date'].apply(lambda x: int(str(x)[-4:]))
# converts the last 4 characters of the string to an integer
The lambda function, is taking the input from the Date and converting it to a year.
You could (and perhaps should) write this more verbosely as:
def convert_to_year(date_in_some_format):
date_as_string = str(date_in_some_format) # cast to string
year_as_string = date_in_some_format[-4:] # last four characters
return int(year_as_string)
df['Date'] = df['Date'].apply(convert_to_year)
Perhaps 'Year' is a better name for this column...