ID   ID_2  END         BEG
1    55    2017-06-30  2016-01-01
1    55    2015-12-31  2015-11-12  --> Gap (required date)
1    88    2008-07-26  2003-02-24
2    19    2014-09-30  2013-05-01
2    33    2013-04-30  2011-01-01  --> Not Gap (overlapping)
2    19    2012-12-31  2011-01-01
2    33    2010-12-31  2008-05-01
2    19    2009-06-30  2009-01-01
2    19    2008-07-26  1980-10-20  --> No actual Gap(required date)

df <- df%>%
  group_by(ID)%>%
  mutate(END_lead = lead(END))

df$FLAG <- df$BEG - days(1) == df$END_lead

df <- df%>%
 group_by(ID)%>%
 filter(cumsum(cumsum(FLAG == FALSE))<=1)

ID   ID_2  END         BEG
1    55    2015-12-31  2015-11-12
2    19    2008-07-26  1980-10-20