df['Date']= df.apply(lambda x: x['start'] + ' '+'to'+ ' '+x['end'],1)
Or
df['Date']=df.groupby(df.index).apply(lambda x:x['start'].str.cat(x['end'], sep=' to '))
start end id Date
0 10/01/2020 11/01/2020 a 10/01/2020 to 11/01/2020
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