SQL Server 2017

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CREATE TABLE T1
    ([Asset_Id] int, [Trailer_Id] int, [AssignStart] datetime, [AssignEnd] datetime)
;
    
INSERT INTO T1
    ([Asset_Id], [Trailer_Id], [AssignStart], [AssignEnd])
VALUES
    (37124, 32607, '2018-04-19 08:55:00', '2018-05-05 10:00:00.000'),
    (37124, 32607, '2018-05-05 11:23:00', NULL),
    (33000, 30000, '2018-04-01 15:00:00', '2018-04-15 10:30:00.000'),
    (34000, 31000, '2018-04-05 10:00:00', '2018-04-10 09:30:00.000'),
    (34000, 32500, '2018-04-10 09:31:00', NULL),
    (37000, 32600, '2018-04-19 08:55:00', '2018-04-25 08:30:00.000'),
    (37000, 32600, '2018-04-25 09:23:00', '2018-04-25 10:00:00.000'),
    (37000, 32600, '2018-04-25 11:23:00', '2018-04-30 15:00:00.000'),
    (37000, 32600, '2018-04-30 16:15:00', '2018-04-30 17:30:00.000'),
    (37000, 32600, '2018-04-30 18:23:00', NULL),
    (38000, 36000, '2018-05-01 10:00:00', '2018-05-10 06:30:00.000'),
    (38000, 36000, '2018-05-15 09:00:00', '2018-05-20 11:00:00.000'),
    (38000, 36000, '2018-05-20 12:00:00', NULL),
    (33000, 30000, '2018-05-01 10:00:00', NULL)
;

SELECT 
  [Asset_Id], [Trailer_Id], [AssignStart], [AssignEnd]
  ,next_AssignStart
  ,IsNUll(DATEDIFF(DAY,[AssignEnd],next_AssignStart),0) as diff_days
FROM
(
SELECT
    [Asset_Id], [Trailer_Id],T1.[AssignStart], [AssignEnd]
    --,LEAD([AssignStart],1,[AssignStart]) OVER(PARTITION BY [Asset_Id], [Trailer_Id] ORDER BY [AssignStart]) as next_AssignStart
    ,OA.[AssignStart] as next_AssignStart
FROM
   T1
   OUTER APPLY
   (SELECT TOP(1) T2.[AssignStart]
      FROM T1 as T2
      WHERE T1.[Asset_Id] = T2.[Asset_Id]
          AND T1.[Trailer_Id] = T2.[Trailer_Id] 
          AND T1.[AssignStart]<T2.[AssignStart] 
      ORDER BY T2.[AssignStart] ASC 
   )OA
)A
ORDER BY [Asset_Id], [Trailer_Id], [AssignStart], [AssignEnd]

SELECT 
  [Asset_Id], [Trailer_Id]
  ,MIN([AssignStart]) as [AssignStart]
  --,MAX(isnull([AssignEnd],[AssignStart])) as [AssignEnd]
  --,MAX([AssignStart]) as maxAssignStart
  ,CASE WHEN MAX(isnull([AssignEnd],[AssignStart])) = MAX([AssignStart]) THEN NULL ELSE MAX(isnull([AssignEnd],[AssignStart])) END as [AssignEnd]
FROM
(
SELECT
    [Asset_Id], [Trailer_Id], T1.[AssignStart], [AssignEnd]
    --,LEAD([AssignStart],1,[AssignStart]) OVER(PARTITION BY [Asset_Id], [Trailer_Id] ORDER BY [AssignStart]) as next_AssignStart
    ,OA.[AssignStart] as next_AssignStart
FROM
   T1
   OUTER APPLY
   (SELECT TOP(1) T2.[AssignStart]
      FROM T1 as T2
      WHERE T1.[Asset_Id] = T2.[Asset_Id]
          AND T1.[Trailer_Id] = T2.[Trailer_Id] 
          AND T1.[AssignStart]<T2.[AssignStart] 
      ORDER BY T2.[AssignStart] ASC 
   )OA
)A
GROUP BY [Asset_Id], [Trailer_Id], IsNUll(DATEDIFF(DAY,[AssignEnd],next_AssignStart),0)
ORDER BY [Asset_Id], [Trailer_Id],[AssignStart]--,[AssignEnd]

Asset_Id	Trailer_Id	AssignStart	AssignEnd	next_AssignStart	diff_days
33000	30000	2018-04-01 15:00:00.000	2018-04-15 10:30:00.000	2018-05-01 10:00:00.000	16
33000	30000	2018-05-01 10:00:00.000	null	null	0
34000	31000	2018-04-05 10:00:00.000	2018-04-10 09:30:00.000	null	0
34000	32500	2018-04-10 09:31:00.000	null	null	0
37000	32600	2018-04-19 08:55:00.000	2018-04-25 08:30:00.000	2018-04-25 09:23:00.000	0
37000	32600	2018-04-25 09:23:00.000	2018-04-25 10:00:00.000	2018-04-25 11:23:00.000	0
37000	32600	2018-04-25 11:23:00.000	2018-04-30 15:00:00.000	2018-04-30 16:15:00.000	0
37000	32600	2018-04-30 16:15:00.000	2018-04-30 17:30:00.000	2018-04-30 18:23:00.000	0
37000	32600	2018-04-30 18:23:00.000	null	null	0
37124	32607	2018-04-19 08:55:00.000	2018-05-05 10:00:00.000	2018-05-05 11:23:00.000	0
37124	32607	2018-05-05 11:23:00.000	null	null	0
38000	36000	2018-05-01 10:00:00.000	2018-05-10 06:30:00.000	2018-05-15 09:00:00.000	5
38000	36000	2018-05-15 09:00:00.000	2018-05-20 11:00:00.000	2018-05-20 12:00:00.000	0
38000	36000	2018-05-20 12:00:00.000	null	null	0

Asset_Id	Trailer_Id	AssignStart	AssignEnd
33000	30000	2018-04-01 15:00:00.000	2018-04-15 10:30:00.000
33000	30000	2018-05-01 10:00:00.000	null
34000	31000	2018-04-05 10:00:00.000	2018-04-10 09:30:00.000
34000	32500	2018-04-10 09:31:00.000	null
37000	32600	2018-04-19 08:55:00.000	null
37124	32607	2018-04-19 08:55:00.000	null
38000	36000	2018-05-01 10:00:00.000	2018-05-10 06:30:00.000
38000	36000	2018-05-15 09:00:00.000	null